1.12 Fractions: multiplication of mixed numerals

$1\frac{1}{8}\cdot 4\frac{2}{3}$

Convert each mixed number to an improper fraction.

$1\frac{1}{8}=\frac{8\cdot 1+1}{8}=\frac{9}{8}$

$4\frac{2}{3}=\frac{4\cdot 3+2}{3}=\frac{\text{14}}{3}$

$\frac{\stackrel{3}{\cancel{9}}}{\underset{4}{\cancel{8}}}\cdot \frac{\stackrel{7}{\cancel{14}}}{\underset{1}{\cancel{3}}}=\frac{3\cdot 7}{4\cdot 1}=\frac{\text{21}}{4}=5\frac{1}{4}$

$\text{16}\cdot 8\frac{1}{5}$

Convert $8\frac{1}{5}$ to an improper fraction.

$8\frac{1}{5}=\frac{5\cdot 8+1}{5}=\frac{\text{41}}{5}$

$\frac{16}{1}\cdot \frac{41}{5}$ .

There are no common factors to divide out.

$\frac{\text{16}}{1}\cdot \frac{\text{41}}{5}=\frac{\text{16}\cdot \text{41}}{1\cdot 5}=\frac{\text{656}}{5}=\text{131}\frac{1}{5}$

$9\frac{1}{6}\cdot \text{12}\frac{3}{5}$

Convert to improper fractions.

$9\frac{1}{6}=\frac{6\cdot 9+1}{6}=\frac{\text{55}}{6}$

$\text{12}\frac{3}{5}=\frac{5\cdot \text{12}+3}{5}=\frac{\text{63}}{5}$

$\frac{\stackrel{\text{11}}{\cancel{55}}}{\underset{2}{\cancel{6}}}\cdot \frac{\stackrel{\text{21}}{\cancel{63}}}{\underset{1}{\cancel{5}}}=\frac{\text{11}\cdot \text{21}}{2\cdot 1}=\frac{\text{231}}{2}=\text{115}\frac{1}{2}$

$\begin{array}{ccc}\hfill \frac{11}{8}\cdot 4\frac{1}{2}\cdot 3\frac{1}{8}& =& \frac{11}{8}\cdot \frac{\stackrel{3}{\cancel{9}}}{\underset{1}{\cancel{2}}}\cdot \frac{\stackrel{5}{\cancel{10}}}{\underset{1}{\cancel{3}}}\hfill \\ & =& \frac{11\cdot 3\cdot 5}{8\cdot 1\cdot 1}=\frac{165}{8}=20\frac{5}{8}\hfill \end{array}$